**Concept:**

A small block of mass m is on a frictionless table and is attached to a horizontal spring. The spring has stiffness k_{s} and a relaxed length L. The other end of the spring is fastened to a fixed point at the center of the table. The block slides on the table in a circular path of radius R > L. How long does it take for the block to go around once?

1. T = √ 3π^{2}mL^{2} / k_{s}R^{2}

2. T = √ 4πmR / k_{s}L

3. T = √ 4π^{2}mR^{2} / k_{s}L

4. T = √ 4πmR / k_{s }(R − L)

5. T = √ 4π^{2}mR^{2} / k_{s}(R − L)^{2}

6. T = √ 2πmR / k_{s}(R − L)

7. T = √ 3π^{2}mR^{2} / k_{s}(R − L)

8. T = √ 4π^{2}mR / k_{s}(R − L)

9. T = √ 4πmR / k_{s}(L − R)

10. T = √ 4π^{2}mR / k_{s}(L − R)

Watch Solution

A 3 kg mass slides without friction along the ground at 12 m/s. If the mass contacts a spring, with a force constant of 100 N/m, compresses the spring to a maximum extent, and is then propeled in the opposite direction, how long is the mass in contact with the spring for?

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A vertical spring supports a 5 kg mass at equilibrium by stretching 3 cm. How far would the same spring have to stretch to support a 7 kg mass at equilibrium?

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A mass-spring system has a period on Earth of 1.7 s. On the moon, where gravity is about one-sixth that of the Earth, what is the period of the spring?

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A simple design for a bathroom scale is to place a platform to stand on atop a spring. If you want the scale to be able to measure weights up to 1500 N, and the scale needs to be 3 cm tall, what is the minimum spring constant required for the scale to work?

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